Effect of humidity on contact electrification due to collision between spherical particles

Effect of humidity on contact electrification due to collision between spherical particles Effect of humidity on contact electrification due to collision between spherical particles L Xie, N Bao, Y Ji[.]

Effect of humidity on contact electrification due to collision between spherical particles

L Xie, N Bao, Y Jiang, and J Zhou

Citation: AIP Advances 6, 035117 (2016); doi: 10.1063/1.4944831

View online: http://dx.doi.org/10.1063/1.4944831

View Table of Contents: http://aip.scitation.org/toc/adv/6/3

Published by the American Institute of Physics

Effect of humidity on contact electrification due

to collision between spherical particles

L Xie,aN Bao, Y Jiang, and J Zhoua

College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu,

China, 730000 and Key Laboratory of Mechanics on Environment and Disaster

in Western China, Ministry of Education, Lanzhou University, Lanzhou, Gansu,

China, 730000

(Received 8 October 2015; accepted 13 March 2016; published online 22 March 2016)

This paper reports an experimental study of the contact electrification (CE) that happens when glass spheres of identical materials collide under different ambient relative humidity (RH) conditions The experimental results indicate that the net charge on a sphere from a single collision is significantly altered by varying the RH level; the charge increases with increasing RH at low humidity, and then decreases

at high RH conditions The net charge reaches a maximum in the 20%–40% RH range To explain the dependence of the CE on RH, we propose a model which yields predictions in agreement with the experimental data The model also reveals how CE can be affected by temperature and surface absorption energy C 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx.doi.org/10.1063/1.4944831]

I INTRODUCTION

Ancient Greeks knew that certain objects, such as rods of amber, after being rubbed with cat’s fur were able to attract light objects like feathers;1this is possibly the earliest record of triboelectrifi-cation or contact electrifitriboelectrifi-cation (CE).2Around 600 BC, Thales of Miletus made a series of observa-tions on static electricity, but he believed the friction rendered the electrified object magnetic.1Later studies indicated that friction/rubbing is not a necessary condition to generate charges on contacting surfaces.2We still do not fully understand how and why such charge generation occurs,3 , 4although considerable progress has been made, such as by considering the role of mechanochemistry6,7and the difference of the composite between the surface and the bulk,2 , 4 , 5 , 8 to more closely reveal the

CE charging mechanism Many researchers have suggested that moisture adsorbed on the surface plays a role in CE9and the related ambient humidity is also thought to be particularly important for surface charging.10McCarty and Whitesides reported a study on the CE of ionic electrets, in which they elaborated on the role of water in CE and proposed a mechanism based on the theory of the electric double layer to explain charge transfer under ambient environments with different humidity levels.11 Whatever the charging mechanism is, there is considerable evidence suggesting that RH

affects the CE.12

Much work has investigated the effect of ambient RH once.9 , 10 , 13 – 18However, existing studies significantly disagree about the effect of RH on CE: some results show that CE increases with increasing RH,9others show that CE decreases as RH is increased,14–17and more still state as RH increases, CE increases at lower RH, followed by decreases at higher RH.18In addition, the results

of Refs.19and20show that the dependence of CE on RH is related to the materials properties However, in their investigation on the effect of RH on CE in gas-solid fluidized beds, Giffin and Mehrani found that the charge or charge-mass ratio did not follow any of the three above-mentioned trends.21Not only is the CE between two materials affected by RH, but also the net surface charges carried on some isolated metals or non-crystals will build up when RH increases.22,23

a Corresponding authors, e-mail: xieli@lzu.edu.cn , zhoujun@lzu.edu.cn

035117-2 Xie et al. AIP Advances 6, 035117 (2016)

In general, the natural environment is not completely dry, therefore usually a thin water film

or island patch will adhere to solid surfaces of hydrophilic materials.11 , 24Therefore, it is necessary

to investigate the dependence of CE on RH However, for most existing CE experimental results, the amount of net charge carried on a particle was determined by measuring the charge-to-mass ratio and size distribution of bulk samples of grains in a grain flow.25It is difficult to distinguish the role of moisture on the CE In this paper, we carried out an experiment to observe the CE due to

a single collision between two spherical particles in identical materials under different RH, which can identify the effect of RH on CE, and a model is proposed to reveal how and why the contact electrification depends on RH

II EXPERIMENTS OF CE UNDER DIFFERENT RH

The instrument used to measure of the CE is detailed in Ref.26and is therefore only briefly introduced here Our experiment is conducted in a glass container with a metal gauze adhered

to inside wall to shield external electrostatic fields, as depicted in Fig 1(a) A Faraday cup is placed at the bottom of the container A target sphere (sphere 2 in Fig 1(a)) with radius R2 is fixed in the Faraday cup An incident sphere (sphere 1 in Fig 1(a)) with a radius R1 falls from

a height H to collide with the target sphere The relative impact velocity, v, can be calculated

by v = 2gH, in which g = 9.8m2/s The incident sphere will rebound out of the Faraday cup after it collides with the target sphere The charges carried by the target sphere can be observed

as the Faraday cup is connected to an electrometer (Type: Keithley 6517A, USA Accuracy: 1pC

FIG 1 (a) Schematic of instrument in the collision experiment to study CE by collision between two spheres; (b) Time series of the net charge of an incident sphere falling into a Faraday cup without colliding with a target sphere, and (c) the time series of the net charge carried by a target sphere with a radius of 10 mm impacted by an incident sphere with a radius of

4 mm, in which the impact speed is 3.96m /s, and the relative humidity and temperature were 46.9% and 294K, respectively.

Range: 0–20nC) The glass container is filled with pure Nitrogen gas before the experiments To change the RH in our experiment, we sprayed water vapor into the glass container by a humidi-fier (Type: YADUSC-M019, China) A thermohygrometer (Type: Testo635-1, Germany Accuracy: 0.1%, Range: 10%–80%) is used to measure the RH The spheres used in the experiments are soda-lime glass with radii ranging from 1mm to 10mm The spheres were washed by tap water, distilled water, and alcohol in turn to eliminate any contamination, and were dried for 8 hours before experiments For each given RH, v, R1and R2, 16-24 trials were done

After the incident sphere is released, it is possible that it becomes electrified due to rubbing with the metal gate and due to rubbing with moist Nitrogen during the free falling process, which

is the initial net charge of the incident sphere in our experiment The initial charges of the incident spheres were measured by letting the incident spheres fall freely into an empty Faraday cup as shown in FIG.1(b) For comparison, Fig.1(c)displays the typical result of the net charge carried

by a target sphere after a single collision It can be seen that net charges carried by a target sphere due to a single collision (Fig 1(c)) are much higher than the initial net charge (Fig.1(b)) due to rubbing with the metal gate and moist Nitrogen Therefore, we neglect the effect of the initial charge

on collision-induced CE in this paper

The outliers of raw data were eliminated by the extreme studentized deviate (ESD) test by choosing the significant level 0.05.27The change in typical net charges with respect to ambient RH

is shown in Fig.2, in which the relative impact velocity is 3.13m/s and the radius of the incident and target particles are 5mm and 10mm, respectively From Fig.2, it can be seen that the amount of net charge carried on the target particle is random at a given RH However, the mean net charge of target spheres increases with increasing ambient RH when the RH is lower, while at higher ambient RH the mean of net charge of the target spheres decreases as the ambient RH is increased The mean net charge value reaches a maximum value at the ambient RH in the region (20%, 40%) shown as red circles in Fig.2, which has the same trend as found by Pence, et al.18This increase-then-decrease trend was also observed for different incident and target particle sizes and relative collision veloc-ities, as presented in Figs.3(a)-3(b) Figs.3(c)-3(d)shows the change of the standard deviations of the net charge amount of target spheres with respect to ambient RH for the different target particle sizes, particle radius ratio and the relative collision velocity

III MODEL OF CE UNDER VARIOUS RH CONDITIONS

As reported by Harper, many materials are hydrophilic and have thin layers of water molecules

on their surfaces.28 , 29Because of impurities in the insulator, surface states, and defects in the chem-ical structure, the surfaces of insulators probably consist of some ionic groups, such as a lattice of oxygen atoms.30Because of the existence of these ionic groups, an electric double layer comprising

FIG 2 Results of net charges carried by a target sphere under di fferent relative humidity, in which the relative impact velocity is 3.13m /s and the radius of the incident sphere and target sphere are 5mm and 10mm, respectively “ ⃝ ” denotes the measured data and red circle denotes mean values.

035117-4 Xie et al. AIP Advances 6, 035117 (2016)

FIG 3 Dependence of mean value and standard deviation of net charges carried by target spheres on relative humidity, under

di fferent sphere sizes, radius ratios, and relative impact velocities.

a stern layer and a diffuse layer will form on the insulator surface,11 , 29 , 31 as shown in Fig 4(a) When two solid surfaces with electric double layers are brought into contact, the surface electric double layers will also be brought into contact.11 , 29In Ref.11, McCarty and Whitesides proposed an experimentally-validated ion transfer mechanism to explain CE for ionic electrets in detail, and they posited that counter ions in the stern layer play an important role in CE

Here, we proposed a model to explain why counter ions in the stern layer play an important role

in CE, and, further, to explain why the dependence of CE on ambient RH is observed differently by

different authors, as reported in Refs.9,10, and13–18 In the case of collision contact, the contact force acting on the incident and target sphere contact surfaces could distort the electric double layers The diffuse layer is liquid-like and is easily forced aside due to collision, while the stern layer sticks to the solid surface firmly Therefore, the stern layers on the two spheres’ surfaces will

be involved in the collision contact process.11Including counter ions in the stern layer and original surface patches of spheres, there are two kinds of surface sites brought into contact as shown in Fig.4(b)

For incident and target spheres of the same material, the surface properties are statistically iden-tical, but the deformations of the two contacting surfaces are different because of the different sizes between both spheres during the collision process Therefore, the number densities of counter ions bound on the two contacting surfaces show different trends, which may provide the driving force for counter ion transfer between the two contacting surfaces The counter ions adsorbed on one surface transfer to the other surface, and they can be regarded as donors as reported in Ref.12 Because the distributions of the counter ions and the original surface patches could be different on the two contact surfaces, the counter ion transfer occurs when one counter-ion site of one surface meets the original sites (named acceptors) on the other surface during the collision The mean number of counter ions transferred from one contacting surface to the other one can be calculated following Ref 32; these numbers are not equal because of the differences in the areas that are brought into contact during collision of the two spheres We refer to the incident sphere and target sphere as sphere 1 and sphere 2, respectively According to Refs.32and33, the net number of counter ions transferred to sphere 2, ∆N , of the donors between the two surfaces of spheres 1 and 2 can be

FIG 4 Schematic of (a) the electric double layer on a sphere surface, and (b) charge sites and their distribution on the sphere surface.

calculated by the following expression,

∆N= α12ND1

NA2

N2

−α21ND2

NA1

N1

(1) Where ND1and NA1are, respectively, the numbers of donors and acceptors on the contacting area of sphere 1, and ND2and NA2are, respectively, the number of donors and acceptors on the con-tacting area of sphere 2 Let N1and N2denote the total number of sites that are possible to give or accept charges on the contacting areas of sphere 1 and 2, respectively, so that N1= ND1+ NA1and

N2= ND2+ NA2 αi j, is the probability that a charge will be transferred from surface i to surface

j (i, j= 1,2), which depends on the energy difference between the donors and acceptors, and the ambient temperature Because the two contacting spheres are of identical material, we assume that

α12= α21= α, and α = 0.5 (see Ref.32)

Baytekin, et al., pointed out that both the number of donors and acceptors are stochastic vari-ables and obey the binomial distribution.33Therefore, the number of the net charges from contact surface of sphere 2 to that of sphere 1 is also a stochastic variable, the mean value of which can be obtained by taking the average on both sides of Eq (1), i.e

⟨∆N⟩ = α ⟨ND1NA2⟩

N2

−⟨ND2NA1⟩

N1



(2)

In which⟨·⟩ denotes a stochastic average of a random variable Usually, the number of donors on surface 1 is independent from the number of the acceptors on surface 2 Assume the probability

of donors appearing on surface 1 and surface 2 are pD1 and pD2, respectively Thus, ⟨ND1NA2⟩

= ⟨ND1⟩⟨NA2⟩ = pD1N1(N2− pD2N2) and ⟨ND2NA1⟩ = ⟨ND2⟩⟨NA1⟩ = pD2N2(N1− pD1N1) Accord-ing to the two-phase equilibrium model presented by Hogue, et al.,29the number of counter ions,

035117-6 Xie et al. AIP Advances 6, 035117 (2016)

i.e the number of donors, can be calculated by formula (3) as follows,

(kBT/λ3) (Π/P) exp (ξ0/kBT)+ 1 (i= 1,2) (3) Where kB is Boltzmann’s constant (kB= 1.38 × 10−23 JK−1), and T denotes the ambient temper-ature λ3= [2πmkB]−3/2, in which m is the mass of a charge and h is Planck’s constant (h

= 6.63 × 10−34Js) Π =∞

1 exp−q2t/ (4πz0ε0kBT)/t2dt, where z0 is the thickness of the water film and ε0is the permittivity, and q is the amount of charges carried on an ion ξ0is the adsorption energy of the solid surface and P is the vapor pressure For a given ambient RH and temperature, the vapor pressure P can be calculated by the expression P= RH × Ps/100,34where Psdenotes the saturated vapor pressure Therefore, we have ⟨NDi ⟩

(kBT /λ 3)(Π/P) exp(ξ 0 /kBT )+1, which means

(kBT/λ3) (Π/P) exp (ξ0/kBT)+ 1 (4) Because the two spheres are of identical material, it is assumed that two sphere surfaces have the same number density of sites, n Therefore, N1= A1n and N2= A2n, in which A1and A2are the collision contact areas of spherical caps on spheres 1 and 2, respectively Therefore, the mean value of the net number of transferred donors is⟨∆N⟩ = αnpD1(1 − pD1) (A1− A2), from which the net charges,⟨∆Q⟩, carried by sphere 2 can be calculated by formula (5), after the collision between spheres 1 and 2,

⟨∆Q⟩ = αnqpD1(1 − pD1) (A1− A2) (5)

in which pD1 is given by formula (4) and A1and A2 are calculated by the formulas in Ref.32 Based on (4) and (5), it is obvious that the amount of net charge transferred between the two contacting surfaces is dependent on the ambient RH, temperature T , and adsorption energy ξ0 Here, according to the Langmuir isotherm,30it is assumed that one site can only adsorb one ion carrying one elementary charge, i.e q= 1.6 × 10−19C Lee and Pantano found there were 7.2 dangling bonds per nm2 on the fracture surface of glass.35 Because dangling bonds may form donors or accep-tors, we assume the number density n in (5) be of the same order as that of dangling bonds, i.e

n= 1.0 × 1018/m2 And z0is taken as 3.2 × 10−8m, which is the effective van der Waals diameter of one hundred water molecules, as reported in Ref.29 With the above-mentioned parameters given, the amount of net charge transferred between the two contact spheres can be calculated for different ambient RH and temperature Fig.5 shows the dependence on RH for the net charge amount due

to collision, compared with the results given by the proposed model (i.e the formula (5)) in this paper, in which R1= 5mm, R2= 10mm, and v = 3.13m/s It can be seen that the CE depends on the ambient RH and the absorption energy of the surface For lower absorption energy, the amount

FIG 5 Dependence of net charges of CE due to collision on ambient RH, which are compared with the results given by the proposed model, i.e formula ( 5 ) Here, hydrogen ions, H +, mass of 1.67 × 10−27 kg, are assumed to be the charge carriers that are transferred between the two contacting surfaces.

of net charge arising from collision increases with increasing RH at lower RH ranges and decreases

as RH increases at relatively higher RH ranges, which agrees with our experimental results and the results observed by Pence, et al.18Based on the proposed model, it is found in Fig.5that for higher absorption energy the amount of net charges due to collision decrease with increasing RH, which agrees with the results in Refs.14–17

Examining formula (5), and it can be found that the amount of net charge transferred between two contact surfaces is a quadratic function of the probability pD1of donors on the surface, which

is dependent on ambient RH, temperature T , and the adsorption energy ξ0 Therefore, for a given

ξ0and temperature T , if pD1lies in [0, 0.5] with increasing the ambient RH, the amount of CE monotonically increases with ambient RH If pD1lies in [0.5, 1], ambient RH conditions, CE mono-tonically decreases with ambient RH; otherwise, if pD1goes through 0.5 with increasing ambient

RH, CE would be a function of RH with a maximum

IV CONCLUSIONS

In conclusions, we investigated the ambient RH dependence of CE by conducting collision experiments between two glass spheres, and proposed a model for predicting the amount of net charge due to collision, which is capable of predicting three kinds of existing experiment results regarding the dependence of CE on ambient RH The proposed model can yield results that are in agreement with those of our experiments The proposed model is achieved by taking the probability

pD1of donors on a solid surface, which is covered with an electric double layer, as a function of ambient RH, temperature T , and the adsorption energy ξ0 In addition, it is worthy of pointing out that in our calculation we used H+as donors because Pence, et al H+is important for CE under

water surface,18which need further study to valid it

ACKNOWLEDGEMENTS

This research is supported by Innovative Research Group of the National Natural Science Foundation of China (No 11421062) and by key grant of the National Natural Science Foundations

of China (No 51435008) and by grants of the National Natural Science Foundations of China (Nos.11472122, 11272139) The authors would like to express their sincere appreciation of this support

1 J V Stewart, Intermediate Electromagnetic Theory (World Scientific, 2001), p 50.

2 M W Williams, American Scientist 100, 316 (2012).

3 D J Lacks and R M Sankaran, J Phys D 44, 453001 (2011).

4 M W Williams, AIP Advances 2, 010701 (2012).

5 M W Williams, Physical Science International Journal 5, 88 (2015).

6 T A L Burgo, T R D Ducati, K R Francisco, K J Clinckspoor, F Galembeck, and S E Galembeck, Langmuir 28, 7407 (2012).

7 L B da SilveiraBalestrin, D S da Silvaand, and F Galembeck, Proc ESA Annual Meeting on Electrostatics (2014).

8 L Xie, P F He, Jun Zhou, and D J Lacks, J Phys D 47, 215501 (2014).

9 J A Wiles, M Fialkowski, M R Radowski, G M Whitesides, and B A Grzybowski, J Phys Chem B 108, 20296 (2004).

10 K Hiratsuka and K Hosotani, Tribol Int 55, 87 (2012).

11 L S McCarty and G M Whitesides, Angew Chem Int Ed 47, 2188 (2008).

12 J Lowell and A C Rose-Innes, Adv Phys 29, 947 (1980).

13 E.M Ramer and H.R Richards, Text Res J 38, 28 (1968).

14 S Nith and T Nguyen, J Electrost 21, 99 (1988).

15 W D Greason, J Electrost 49, 245 (2000).

16 T Nomura, T Satoh, and H Masuda, Powder Technol 135-136, 43 (2003).

17 H Nouri, N Zouzou, E Moreau, L Dascalescu, and Y Zebboudj, J Electrost 70, 20 (2012).

18 S Pence, V J Novotny, and A F Diaz, Langmuir 10, 592 (1994).

19 A Elajnaf, P Carter, and G Rowley, Eur J Pharm Sci 29, 375 (2006).

20 S Matsusaka, H Maruyama, T Matsuyama, and M Ghadiri, Chem Eng Sci 65, 5781 (2010).

21 A Gi ffin and P Mehrani, Powder Technol 235, 368 (2013).

22 A Elajnaf, P Carter, and G Rowley, Eur J Pharm Sci 29, 375 (2006).

23 K Hiratsuka and K Hosotani, Tribol Int 55, 87 (2012).

24 Y Awakuni and J H Calderwood, J Phys D 5, 1038 (1972).

25 S.R Waitukaitis and H M Jaeger, Rev Sci.Instrum 84, 025104 (2013).

035117-8 Xie et al. AIP Advances 6, 035117 (2016)

26 L Xie, N Bao, Y Jiang, K Han, and J Zhou, Rev Sci.Instrum 87, 014705 (2015).

27 B Rosner, Tchnometrics 25, 165 (1983).

28 W.R Harper, Contact and frictional electrification (Laplacian Press, Morgan Hill, Calif., 1998).

29 M.D Hogue, C.R Buhler, C.I Calle, T Matsyama, W Luo, and E.E Groop, J Electrost 61, 259 (2004).

30 I Langmuir, J Am Chem Soc 40, 1361 (1918).

31 D C Grahame, Chem Rev 41, 441 (1947).

32 L Xie, G Li, N Bao, and J Zhou, J Appl Phys 113, 184908 (2013).

33 H T Baytekin, A Z Patashinski, M Branicki, B Baytekin, S Soh, and B A Grzybowski, Science 333, 308 (2011).

34 R H Perry, D W Green, and J O Maloney, Perry’s Chemical Engineers’ Handbook, 7th ed (McGraw-Hill, 1997), Eqn 12-7, ISBN: 0-07-049841-5.

35 E A Leed and C G Pantano, J Non-Cryst Solids 325, 48 (2003).